6x^2-18x=-2x^2-3x-7

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Solution for 6x^2-18x=-2x^2-3x-7 equation: 


Simplifying
6x2 + -18x = -2x2 + -3x + -7

Reorder the terms:
-18x + 6x2 = -2x2 + -3x + -7

Reorder the terms:
-18x + 6x2 = -7 + -3x + -2x2

Solving
-18x + 6x2 = -7 + -3x + -2x2

Solving for variable 'x'.

Reorder the terms:
7 + -18x + 3x + 6x2 + 2x2 = -7 + -3x + -2x2 + 7 + 3x + 2x2

Combine like terms: -18x + 3x = -15x
7 + -15x + 6x2 + 2x2 = -7 + -3x + -2x2 + 7 + 3x + 2x2

Combine like terms: 6x2 + 2x2 = 8x2
7 + -15x + 8x2 = -7 + -3x + -2x2 + 7 + 3x + 2x2

Reorder the terms:
7 + -15x + 8x2 = -7 + 7 + -3x + 3x + -2x2 + 2x2

Combine like terms: -7 + 7 = 0
7 + -15x + 8x2 = 0 + -3x + 3x + -2x2 + 2x2
7 + -15x + 8x2 = -3x + 3x + -2x2 + 2x2

Combine like terms: -3x + 3x = 0
7 + -15x + 8x2 = 0 + -2x2 + 2x2
7 + -15x + 8x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
7 + -15x + 8x2 = 0

Factor a trinomial.
(7 + -8x)(1 + -1x) = 0


Subproblem 1
Set the factor '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0.875, 1}

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